Approxımatıon Propertıes Of A Generatıng Functıons Type Generalızatıon Of Meyer-Könıg And Zeller Operators


Thesis Type: Post Graduate

Institution Of The Thesis: Gazi Üniversitesi, Fen Bilimleri Enstitüsü, Turkey

Approval Date: 2017

Student: KÜBRA KÜNYELİ

Consultant: OGÜN DOĞRU

Abstract:

This thesis consists of seven chapters. In the first chapter, the definition of linear positive operators and some theorems about their approximation properties have been given. In the second chapter, Meyer-König and Zeller operators and a generalization of theese operators have been given. In the third chapter, the uniform convergence of these operators has been studied with the help of Korovkin Theorem. In the forth chapter, the convergence features of the these operators have been mentioned. In this chapter, in addition, the third and fourth moments obtained for the operators we have examined in this section form the original part of thesis. In the fifth chapter, the approximation order of some generalizations of Meyer-König and Zeller operators has been obtained by the aid of Peetre-K functional and modulus of continuity for continuous function. On the other hand, this section contains the original part of the thesis. It involves a proof for a Voronovkaja-type theorem by obtaining the third and forth momentums of said operators, which gives a better approximation order. In the sixth chapter, the generalization of r-th order of the operators has been introduced. Finally, in the seventh chapter, the application of these operators to differential equations has been given.